Question

A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the​ exam, scores are normally distributed with

mu equalsμ=519519.

The teacher obtains a random sample of

20002000

​students, puts them through the review​ class, and finds that the mean math score of the

20002000

students is

525525

with a standard deviation of

114114.

Complete parts​ (a) through​ (d) below.

​(a) State the null and alternative hypotheses. Let

muμ

be the mean score. Choose the correct answer below.

A.

Upper H 0 : mu less than 519H0: μ<519​,

Upper H 1 : mu greater than 519H1: μ>519

B.

Upper H 0 : mu equals 519H0: μ=519​,

Upper H 1 : mu not equals 519H1: μ≠519

C.

Upper H 0 : mu greater than 519H0: μ>519​,

Upper H 1 : mu not equals 519H1: μ≠519

D.

Upper H 0 : mu equals 519H0: μ=519​,

Upper H 1 : mu greater than 519H1: μ>519​(b) Test the hypothesis at the

alpha equalsα=0.100.10

level of significance. Is a mean math score of

525525

statistically significantly higher than

519519​?

Conduct a hypothesis test using the​ P-value approach.

Find the test statistic.

t 0t0equals=nothing

​(Round to two decimal places as​ needed.)

Find the​ P-value.

The​ P-value is

nothing.

​(Round to three decimal places as​ needed.)

Is the sample mean statistically significantly​ higher?

NoNo

YesYes

​(c) Do you think that a mean math score of

525525

versus

519519

will affect the decision of a school admissions​administrator? In other​ words, does the increase in the score have any practical​ significance?

​No, because the score became only

1.161.16​%

greater.

​Yes, because every increase in score is practically significant.

​(d) Test the hypothesis at the

alphaαequals=0.10

level of significance with

nequals=350350

students. Assume that the sample mean is still

525525

and the sample standard deviation is still

114114.

Is a sample mean of

525525

significantly more than

519519​?

Conduct a hypothesis test using the​ P-value approach.

Find the test statistic.

t 0t0equals=nothing

​(Round to two decimal places as​ needed.)

Find the​ P-value.

The​ P-value is

nothing.

​(Round to three decimal places as​ needed.)

Is the sample mean statistically significantly​ higher?

NoNo

YesYes

What do you conclude about the impact of large samples on the​ P-value?

A.

As n​ increases, the likelihood of not rejecting the null hypothesis increases.​ However, large samples tend to overemphasize practically significant differences.

B.

As n​ increases, the likelihood of rejecting the null hypothesis increases.​ However, large samples tend to overemphasize practically insignificant differences.

C.

As n​ increases, the likelihood of rejecting the null hypothesis increases.​ However, large samples tend to overemphasize practically significant differences.

D.

As n​ increases, the likelihood of not rejecting the null hypothesis increases.​ However, large samples tend to overemphasize practically insignificant differences.

Answer 1

Ans:

a)

$H_0:\mu =519$

$H_a:\mu >519$

b)Test statistic:

t=(525-519)/(114/SQRT(2000))

t=2.35

p-value=tdist(2.35,1999,1)=0.009

Reject the null hypothesis.

Yes,Sample mean is statistically significantly​ higher.

c)

Yes, because every increase in score is practically significant.

d)

t=(525-519)/(114/SQRT(350))

t=0.98

p-value=tdist(0.98,349,1)=0.163

No,Sample mean is not statistically significantly​ higher.

Option B is correct.

As n​ increases, the likelihood of rejecting the null hypothesis increases.​ However, large samples tend to overemphasize practically insignificant differences.